{"status": "success", "data": {"description_md": "Point $D$ lies on side $BC$ of $\\triangle ABC$ so that $\\overline{AD}$ bisects $\\angle BAC$. The perpendicular bisector of $\\overline{AD}$ intersects the bisectors of $\\angle ABC$ and $\\angle ACB$ in points $E$ and $F$, respectively. Given that $AB=4$, $BC=5$, $CA=6$, the area of $\\triangle AEF$ can be written as $\\tfrac{m\\sqrt n}p$, where $m$ and $p$ are relatively prime positive integers, and $n$ is a positive integer not divisible by the square of any prime. Find $m+n+p$.\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "

Point D lies on side BC of \\triangle ABC so that \\overline{AD} bisects \\angle BAC. The perpendicular bisector of \\overline{AD} intersects the bisectors of \\angle ABC and \\angle ACB in points E and F, respectively. Given that AB=4, BC=5, CA=6, the area of \\triangle AEF can be written as \\tfrac{m\\sqrt n}p, where m and p are relatively prime positive integers, and n is a positive integer not divisible by the square of any prime. Find m+n+p.

Leading zeroes must be inputted, so if your answer is 34, then input 034. Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 6, "problem_name": "2020 AIME I Problem 13", "can_next": true, "can_prev": true, "nxt": "/problem/20_aime_I_p14", "prev": "/problem/20_aime_I_p12"}}